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PDFPatcher/App/Processor/Imaging/WuQuantize.c
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Having received many constructive comments and bug reports about my previous
C implementation of my color quantizer (Graphics Gems vol. II, p. 126-133),
I am posting the following second version of my program (hopefully 100%
healthy) as a reply to all those who are interested in the problem.
/**********************************************************************
C Implementation of Wu's Color Quantizer (v. 2)
(see Graphics Gems vol. II, pp. 126-133)
Author: Xiaolin Wu
Dept. of Computer Science
Univ. of Western Ontario
London, Ontario N6A 5B7
wu@csd.uwo.ca
Algorithm: Greedy orthogonal bipartition of RGB space for variance
minimization aided by inclusion-exclusion tricks.
For speed no nearest neighbor search is done. Slightly
better performance can be expected by more sophisticated
but more expensive versions.
The author thanks Tom Lane at Tom_Lane@G.GP.CS.CMU.EDU for much of
additional documentation and a cure to a previous bug.
Free to distribute, comments and suggestions are appreciated.
**********************************************************************/
#include<stdio.h>
#define MAXCOLOR 256
#define RED 2
#define GREEN 1
#define BLUE 0
struct box {
int r0; /* min value, exclusive */
int r1; /* max value, inclusive */
int g0;
int g1;
int b0;
int b1;
int vol;
};
/* Histogram is in elements 1..HISTSIZE along each axis,
* element 0 is for base or marginal value
* NB: these must start out 0!
*/
float m2[33][33][33];
long int wt[33][33][33], mr[33][33][33], mg[33][33][33], mb[33][33][33];
unsigned char *Ir, *Ig, *Ib;
int size; /*image size*/
int K; /*color look-up table size*/
unsigned short int *Qadd;
void
Hist3d(vwt, vmr, vmg, vmb, m2)
/* build 3-D color histogram of counts, r/g/b, c^2 */
long int *vwt, *vmr, *vmg, *vmb;
float *m2;
{
register int ind, r, g, b;
int inr, ing, inb, table[256];
register long int i;
for(i=0; i<256; ++i) table[i]=i*i;
Qadd = (unsigned short int *)malloc(sizeof(short int)*size);
if (Qadd==NULL) {printf("Not enough space\n"); exit(1);}
for(i=0; i<size; ++i){
r = Ir[i]; g = Ig[i]; b = Ib[i];
inr=(r>>3)+1;
ing=(g>>3)+1;
inb=(b>>3)+1;
Qadd[i]=ind=(inr<<10)+(inr<<6)+inr+(ing<<5)+ing+inb;
/*[inr][ing][inb]*/
++vwt[ind];
vmr[ind] += r;
vmg[ind] += g;
vmb[ind] += b;
m2[ind] += (float)(table[r]+table[g]+table[b]);
}
}
/* At conclusion of the histogram step, we can interpret
* wt[r][g][b] = sum over voxel of P(c)
* mr[r][g][b] = sum over voxel of r*P(c) , similarly for mg, mb
* m2[r][g][b] = sum over voxel of c^2*P(c)
* Actually each of these should be divided by 'size' to give the usual
* interpretation of P() as ranging from 0 to 1, but we needn't do that here.
*/
/* We now convert histogram into moments so that we can rapidly calculate
* the sums of the above quantities over any desired box.
*/
void
M3d(vwt, vmr, vmg, vmb, m2) /* compute cumulative moments. */
long int *vwt, *vmr, *vmg, *vmb;
float *m2;
{
register unsigned short int ind1, ind2;
register unsigned char i, r, g, b;
long int line, line_r, line_g, line_b,
area[33], area_r[33], area_g[33], area_b[33];
float line2, area2[33];
for(r=1; r<=32; ++r){
for(i=0; i<=32; ++i)
area2[i]=area[i]=area_r[i]=area_g[i]=area_b[i]=0;
for(g=1; g<=32; ++g){
line2 = line = line_r = line_g = line_b = 0;
for(b=1; b<=32; ++b){
ind1 = (r<<10) + (r<<6) + r + (g<<5) + g + b; /* [r][g][b] */
line += vwt[ind1];
line_r += vmr[ind1];
line_g += vmg[ind1];
line_b += vmb[ind1];
line2 += m2[ind1];
area[b] += line;
area_r[b] += line_r;
area_g[b] += line_g;
area_b[b] += line_b;
area2[b] += line2;
ind2 = ind1 - 1089; /* [r-1][g][b] */
vwt[ind1] = vwt[ind2] + area[b];
vmr[ind1] = vmr[ind2] + area_r[b];
vmg[ind1] = vmg[ind2] + area_g[b];
vmb[ind1] = vmb[ind2] + area_b[b];
m2[ind1] = m2[ind2] + area2[b];
}
}
}
}
long int Vol(cube, mmt)
/* Compute sum over a box of any given statistic */
struct box *cube;
long int mmt[33][33][33];
{
return( mmt[cube->r1][cube->g1][cube->b1]
-mmt[cube->r1][cube->g1][cube->b0]
-mmt[cube->r1][cube->g0][cube->b1]
+mmt[cube->r1][cube->g0][cube->b0]
-mmt[cube->r0][cube->g1][cube->b1]
+mmt[cube->r0][cube->g1][cube->b0]
+mmt[cube->r0][cube->g0][cube->b1]
-mmt[cube->r0][cube->g0][cube->b0] );
}
/* The next two routines allow a slightly more efficient calculation
* of Vol() for a proposed subbox of a given box. The sum of Top()
* and Bottom() is the Vol() of a subbox split in the given direction
* and with the specified new upper bound.
*/
long int Bottom(cube, dir, mmt)
/* Compute part of Vol(cube, mmt) that doesn't depend on r1, g1, or b1 */
/* (depending on dir) */
struct box *cube;
unsigned char dir;
long int mmt[33][33][33];
{
switch(dir){
case RED:
return( -mmt[cube->r0][cube->g1][cube->b1]
+mmt[cube->r0][cube->g1][cube->b0]
+mmt[cube->r0][cube->g0][cube->b1]
-mmt[cube->r0][cube->g0][cube->b0] );
break;
case GREEN:
return( -mmt[cube->r1][cube->g0][cube->b1]
+mmt[cube->r1][cube->g0][cube->b0]
+mmt[cube->r0][cube->g0][cube->b1]
-mmt[cube->r0][cube->g0][cube->b0] );
break;
case BLUE:
return( -mmt[cube->r1][cube->g1][cube->b0]
+mmt[cube->r1][cube->g0][cube->b0]
+mmt[cube->r0][cube->g1][cube->b0]
-mmt[cube->r0][cube->g0][cube->b0] );
break;
}
}
long int Top(cube, dir, pos, mmt)
/* Compute remainder of Vol(cube, mmt), substituting pos for */
/* r1, g1, or b1 (depending on dir) */
struct box *cube;
unsigned char dir;
int pos;
long int mmt[33][33][33];
{
switch(dir){
case RED:
return( mmt[pos][cube->g1][cube->b1]
-mmt[pos][cube->g1][cube->b0]
-mmt[pos][cube->g0][cube->b1]
+mmt[pos][cube->g0][cube->b0] );
break;
case GREEN:
return( mmt[cube->r1][pos][cube->b1]
-mmt[cube->r1][pos][cube->b0]
-mmt[cube->r0][pos][cube->b1]
+mmt[cube->r0][pos][cube->b0] );
break;
case BLUE:
return( mmt[cube->r1][cube->g1][pos]
-mmt[cube->r1][cube->g0][pos]
-mmt[cube->r0][cube->g1][pos]
+mmt[cube->r0][cube->g0][pos] );
break;
}
}
float Var(cube)
/* Compute the weighted variance of a box */
/* NB: as with the raw statistics, this is really the variance * size */
struct box *cube;
{
float dr, dg, db, xx;
dr = Vol(cube, mr);
dg = Vol(cube, mg);
db = Vol(cube, mb);
xx = m2[cube->r1][cube->g1][cube->b1]
-m2[cube->r1][cube->g1][cube->b0]
-m2[cube->r1][cube->g0][cube->b1]
+m2[cube->r1][cube->g0][cube->b0]
-m2[cube->r0][cube->g1][cube->b1]
+m2[cube->r0][cube->g1][cube->b0]
+m2[cube->r0][cube->g0][cube->b1]
-m2[cube->r0][cube->g0][cube->b0];
return( xx - (dr*dr+dg*dg+db*db)/(float)Vol(cube,wt) );
}
/* We want to minimize the sum of the variances of two subboxes.
* The sum(c^2) terms can be ignored since their sum over both subboxes
* is the same (the sum for the whole box) no matter where we split.
* The remaining terms have a minus sign in the variance formula,
* so we drop the minus sign and MAXIMIZE the sum of the two terms.
*/
float Maximize(cube, dir, first, last, cut,
whole_r, whole_g, whole_b, whole_w)
struct box *cube;
unsigned char dir;
int first, last, *cut;
long int whole_r, whole_g, whole_b, whole_w;
{
register long int half_r, half_g, half_b, half_w;
long int base_r, base_g, base_b, base_w;
register int i;
register float temp, max;
base_r = Bottom(cube, dir, mr);
base_g = Bottom(cube, dir, mg);
base_b = Bottom(cube, dir, mb);
base_w = Bottom(cube, dir, wt);
max = 0.0;
*cut = -1;
for(i=first; i<last; ++i){
half_r = base_r + Top(cube, dir, i, mr);
half_g = base_g + Top(cube, dir, i, mg);
half_b = base_b + Top(cube, dir, i, mb);
half_w = base_w + Top(cube, dir, i, wt);
/* now half_x is sum over lower half of box, if split at i */
if (half_w == 0) { /* subbox could be empty of pixels! */
continue; /* never split into an empty box */
} else
temp = ((float)half_r*half_r + (float)half_g*half_g +
(float)half_b*half_b)/half_w;
half_r = whole_r - half_r;
half_g = whole_g - half_g;
half_b = whole_b - half_b;
half_w = whole_w - half_w;
if (half_w == 0) { /* subbox could be empty of pixels! */
continue; /* never split into an empty box */
} else
temp += ((float)half_r*half_r + (float)half_g*half_g +
(float)half_b*half_b)/half_w;
if (temp > max) {max=temp; *cut=i;}
}
return(max);
}
int
Cut(set1, set2)
struct box *set1, *set2;
{
unsigned char dir;
int cutr, cutg, cutb;
float maxr, maxg, maxb;
long int whole_r, whole_g, whole_b, whole_w;
whole_r = Vol(set1, mr);
whole_g = Vol(set1, mg);
whole_b = Vol(set1, mb);
whole_w = Vol(set1, wt);
maxr = Maximize(set1, RED, set1->r0+1, set1->r1, &cutr,
whole_r, whole_g, whole_b, whole_w);
maxg = Maximize(set1, GREEN, set1->g0+1, set1->g1, &cutg,
whole_r, whole_g, whole_b, whole_w);
maxb = Maximize(set1, BLUE, set1->b0+1, set1->b1, &cutb,
whole_r, whole_g, whole_b, whole_w);
if( (maxr>=maxg)&&(maxr>=maxb) ) {
dir = RED;
if (cutr < 0) return 0; /* can't split the box */
}
else
if( (maxg>=maxr)&&(maxg>=maxb) )
dir = GREEN;
else
dir = BLUE;
set2->r1 = set1->r1;
set2->g1 = set1->g1;
set2->b1 = set1->b1;
switch (dir){
case RED:
set2->r0 = set1->r1 = cutr;
set2->g0 = set1->g0;
set2->b0 = set1->b0;
break;
case GREEN:
set2->g0 = set1->g1 = cutg;
set2->r0 = set1->r0;
set2->b0 = set1->b0;
break;
case BLUE:
set2->b0 = set1->b1 = cutb;
set2->r0 = set1->r0;
set2->g0 = set1->g0;
break;
}
set1->vol=(set1->r1-set1->r0)*(set1->g1-set1->g0)*(set1->b1-set1->b0);
set2->vol=(set2->r1-set2->r0)*(set2->g1-set2->g0)*(set2->b1-set2->b0);
return 1;
}
Mark(cube, label, tag)
struct box *cube;
int label;
unsigned char *tag;
{
register int r, g, b;
for(r=cube->r0+1; r<=cube->r1; ++r)
for(g=cube->g0+1; g<=cube->g1; ++g)
for(b=cube->b0+1; b<=cube->b1; ++b)
tag[(r<<10) + (r<<6) + r + (g<<5) + g + b] = label;
}
main()
{
struct box cube[MAXCOLOR];
unsigned char *tag;
unsigned char lut_r[MAXCOLOR], lut_g[MAXCOLOR], lut_b[MAXCOLOR];
int next;
register long int i, weight;
register int k;
float vv[MAXCOLOR], temp;
/* input R,G,B components into Ir, Ig, Ib;
set size to width*height */
printf("no. of colors:\n");
scanf("%d", &K);
Hist3d(wt, mr, mg, mb, m2); printf("Histogram done\n");
free(Ig); free(Ib); free(Ir);
M3d(wt, mr, mg, mb, m2); printf("Moments done\n");
cube[0].r0 = cube[0].g0 = cube[0].b0 = 0;
cube[0].r1 = cube[0].g1 = cube[0].b1 = 32;
next = 0;
for(i=1; i<K; ++i){
if (Cut(&cube[next], &cube[i])) {
/* volume test ensures we won't try to cut one-cell box */
vv[next] = (cube[next].vol>1) ? Var(&cube[next]) : 0.0;
vv[i] = (cube[i].vol>1) ? Var(&cube[i]) : 0.0;
} else {
vv[next] = 0.0; /* don't try to split this box again */
i--; /* didn't create box i */
}
next = 0; temp = vv[0];
for(k=1; k<=i; ++k)
if (vv[k] > temp) {
temp = vv[k]; next = k;
}
if (temp <= 0.0) {
K = i+1;
fprintf(stderr, "Only got %d boxes\n", K);
break;
}
}
printf("Partition done\n");
/* the space for array m2 can be freed now */
tag = (unsigned char *)malloc(33*33*33);
if (tag==NULL) {printf("Not enough space\n"); exit(1);}
for(k=0; k<K; ++k){
Mark(&cube[k], k, tag);
weight = Vol(&cube[k], wt);
if (weight) {
lut_r[k] = Vol(&cube[k], mr) / weight;
lut_g[k] = Vol(&cube[k], mg) / weight;
lut_b[k] = Vol(&cube[k], mb) / weight;
}
else{
fprintf(stderr, "bogus box %d\n", k);
lut_r[k] = lut_g[k] = lut_b[k] = 0;
}
}
for(i=0; i<size; ++i) Qadd[i] = tag[Qadd[i]];
/* output lut_r, lut_g, lut_b as color look-up table contents,
Qadd as the quantized image (array of table addresses). */
}
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